Townsend - who has been sent out on loan to eight different clubs to gain some experience - picked up the ball around the half-way line and weaved his way past two defenders before firing in from outside the box.
Spurs coach Steffen Freund said: "It was a great goal. Andros is quick and he's really good with the ball at his feet. It's good to see young players get a chance.
"We have someone who is behind Gareth Bale and that can only be a good thing for the club."